On the Probability of Independent Sets in Random Graphs

Michael Krivelevich, Benny Sudakov, Van H. Vu, Nicholas C. Wormald

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

Abstract

Let k be the asymptotic value of the independence number of the random graph G(n, p). We prove that if the edge probability p(n) satisfies p(n) ≫ n-2/5ln6/5n then the probability that G(n, p) does not contain an independent set of size k - c, for some absolute constant c > 0, is at most exp{ -cn2/(k4p)}. We also show that the obtained exponent is tight up to logarithmic factors, and apply our result to obtain new bounds on the choice number of random graphs. We also discuss a general setting where our approach can be applied to provide an exponential bound on the probability of certain events in product probability spaces.

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalRandom Structures and Algorithms
Volume22
Issue number1
DOIs
Publication statusPublished - Jan 2003
Externally publishedYes

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